In the following number series a wrong number is given. Find out that number 8 18 40 86 178 370 752

Options

A. 178
B. 180
C. 128
D. 156

Answer

To find the wrong number in the series 8, 18, 40, 86, 178, 370, 752, we can analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Series**:
The given series is:
\[ 8, 18, 40, 86, 178, 370, 752 \]

2. **Look for a Pattern**:
We will try to find a relationship between consecutive terms. It seems that each term is derived from the previous term by a certain operation.

3. **Calculate Differences**:
Let's analyze how each term relates to the previous term:
- From 8 to 18:
\[ 18 = 8 \times 2 + 2 \]
- From 18 to 40:
\[ 40 = 18 \times 2 + 4 \]
- From 40 to 86:
\[ 86 = 40 \times 2 + 6 \]
- From 86 to 178:
\[ 178 = 86 \times 2 + 6 \]
- From 178 to 370:
\[ 370 = 178 \times 2 + 14 \]
- From 370 to 752:
\[ 752 = 370 \times 2 + 12 \]

4. **Identify the Anomaly**:
The pattern seems to be multiplying by 2 and then adding an increasing even number (2, 4, 6, 8, ...). However, when we check the term from 86 to 178, we see:
\[ 178 = 86 \times 2 + 6 \quad \text{(this is correct)} \]
But when we check the next term:
\[ 370 = 178 \times 2 + 14 \quad \text{(this should be 180)} \]

5. **Verify the Correct Number**:
If we assume the correct term after 86 should be:
\[ 86 \times 2 + 8 = 180 \]
Then the series should be:
\[ 8, 18, 40, 86, 180, 370, 752 \]

6. **Conclusion**:
The wrong number in the series is **178**. The correct number should be **180**.

### Final Answer:
The wrong number in the series is **178**; it should be **180**.